Physics-based patient-specific models have the potential to support physicians in decision-making during diagnosis and intervention planning.To adapt these models to personalized conditions, patient-specific input parameters should be available. In clinics, the number of measurable input parameters is limited which results in sparse datasets. In addition, patient data are compromised with uncertainty. These uncertain and incomplete input datasets will result in model output uncertainties. By means of a global variance-based sensitivity analysis it can be assessed which uncertain input parameters are most rewarding to measure more accurately for reducing output uncertainty (parameter prioritization) and which irrelevant model parameters can be fixed within their uncertainty domain (parameter fixing). Such an analysis can therefore give directions for input measurement improvement. In this work, we will discuss the role of uncertainty and sensitivity analysis in patient-tailored modeling. In addition, we will present a two-step variance-based sensitivity analysis method for a cardiovascular model with many model parameters. In the first step, we perform a screening method to reduce the parameter input space, followed by generalized polynomial chaos expansion. Furthermore, we will introduce an adaptive generalized polynomial chaos expansion method which is an efficient variance-based sensitivity analysis approach for computationally expensive models and was first introduced by Blatman et al. in the field of structural reliability engineering.